Lena Dunham's character, who she uses as a mouthpiece, has said precisely that she's speaking for a generation of people like her, and later implied it in interviews with the language she uses to describe her show. She's aware but, like many white persons, doesn't correlate it with her whiteness and well-connected upbringing.
http://www.newyorker.com/online/blogs/culture/2012/04/lena-dunham-girls-race.html#ixzz2HtbhmxrC
That's how naive and blind she is, and that's why I loathe junk like Girls. The nonchalant, casual attitude of people like her who "don't notice" minorities (or the complete lack of). The utter lack of black and hispanics people in depicting Prospect Heights (70%+ of the pop.!) doesn't register mentally in her life of privilege. It may just be a show, but Dunham panders to the self-obsessed, passively racist person in NY: the kind who interacts with minorities as little as possible (otherwise it's inconvenient), says he "has a black friend" and therefore can't possibly be racist when behaving in a racist manner, and who quietly becomes upset if ethnic minorities move into her upper-class (white) neighborhood in any significant numbers.